Article

# One-loop BPS amplitudes as BPS-state sums

(Impact Factor: 6.11). 03/2012; 2012(6). DOI: 10.1007/JHEP06(2012)070
Source: arXiv

ABSTRACT

Recently, we introduced a new procedure for computing a class of one-loop
BPS-saturated amplitudes in String Theory, which expresses them as a sum of
one-loop contributions of all perturbative BPS states in a manifestly T-duality
invariant fashion. In this paper, we extend this procedure to all BPS-saturated
amplitudes of the form \int_F \Gamma_{d+k,d} {\Phi}, with {\Phi} being a weak
(almost) holomorphic modular form of weight -k/2. We use the fact that any such
{\Phi} can be expressed as a linear combination of certain absolutely
convergent Poincar\'e series, against which the fundamental domain F can be
unfolded. The resulting BPS-state sum neatly exhibits the singularities of the
amplitude at points of gauge symmetry enhancement, in a chamber-independent
fashion. We illustrate our method with concrete examples of interest in
heterotic string compactifications.

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• "+ n relevant for the expansion (3.15), the summand in (3.20) can be rewritten in terms of elementary functions [19]. "
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